Technique for continuous OFDM demodulation

ABSTRACT

A technique includes receiving a signal that indicates a modulated symbol during a given time slice of the signal. Sliding window frequency transformations of the signal are performed, and each sliding window transformation is associated with a different time interval of the signal. One of the time intervals is selected to correspond to the time slice. The result of the frequency transformation associated with the selected time interval is used to obtain an indication of the demodulated symbol.

BACKGROUND

[0001] The invention generally relates to a technique for continuousdemodulation of Orthogonal Frequency Division Multiplexing (OFDM)signals.

[0002] Many recent implementations of digital wireless communicationsystems (wireless or cable-based systems, for example) use OrthogonalFrequency Division Multiplexing (OFDM) for environments where there arestrong interference or multipath reflections. However, one disadvantageof using OFDM is the use of a Fast Fourier Transform (FFT) and aninverse FFT (IFFT) in the demodulator (for an OFDM transmitter) andmodulator (for an OFDM receiver), respectively. In this manner, thecalculation of the FFT and inverse FFT may add a consider all the amountof complexity to the OFDM transmitter/receiver due to the largeprocessing block that is required on each end of the communication link.

[0003] While OFDM may offer superior performance in fading, interferenceand multipath environments, it is not without its disadvantages. Forexample, one disadvantage that is associated with OFDM is the difficultyin synchronization, a difficulty that may lead to long acquisition timesthat may adversely effect the overall system performance. In thismanner, the OFDM signal includes modulated OFDM symbols. Each symbol, inturn, appears during a particular time slot. Thus, to demodulate theOFDM signal to extract a particular symbol, the demodulation must besynchronized with the time slot. Many OFDM systems use pilot tones forchannel estimation as well as to aid in the synchronization. The OFDMsystems that use the pilot tones modulate or scramble the pilot tones inorder to reduce the transmit peak-to-average power ratio.

[0004] For purposes of maximizing statistical multiplexing gain, manycommunication systems assign subsets of OFDM subcarriers to individualusers, terminals or electrical devices in both the upstream anddownstream directions. In this manner, the data that is associated witha particular user, terminal or electrical device is modulated at theOFDM transmitter via an associated subset of OFDM subcarriers. Theresultant OFDM modulated signal is then modulated via an RF carriersignal, and this carrier modulated signal is transmitted over a wirelesslink (for example) for reception by an OFDM receiver. This OFDMmodulation technique is commonly called OFDMA for Orthogonal FrequencyDivision Multiple Access.

[0005] The FFT is an N point operation, i.e., the FFT is based on a setof N subcarriers. In this manner, for the OFDM receiver, the data thatis assigned to a particular subset of the subcarriers forms an FFT inputvector that is processed via the FFT to produce the demodulated OFDMfrequency coefficients that indicate a particular demodulated OFDMsymbol.

[0006] As noted above, it is possible that some of the OFDM subcarriersmay not be assigned to a particular transmitter. As a result, the blockcomputation of the FFT for OFDM demodulation may involve calculatingfrequency coefficients for subcarriers that are not being used, therebyresulting in inefficient computation of the FFT.

[0007] Thus, there exists a continuing need for a technique orarrangement that addresses one or more of the problems that are statedabove.

BRIEF DESCRIPTION OF THE DRAWING

[0008]FIG. 1 is a schematic diagram of an OFDM receiver according to anembodiment of the invention.

[0009]FIG. 2 is an illustration depicting demodulation of an OFDM signalaccording to an embodiment of the invention.

[0010]FIG. 3 is a flow diagram depicting a technique to demodulate anOFDM signal according to an embodiment of the invention.

[0011]FIG. 4 is a signal flow diagram for the computation of an inverseRadix-two FFT of the prior art.

[0012]FIG. 5 is a signal flow diagram for the computation of a DFTaccording to an embodiment of the invention.

[0013]FIG. 6 is a table depicting a comparison of the demodulationtechnique of the present invention and a demodulation technique of theprior art.

[0014]FIG. 7 is a schematic diagram of a transmitter according to anembodiment of the invention.

[0015]FIG. 8 is a flow diagram depicting an OFDM symbol generationtechnique according to an embodiment of the invention.

[0016]FIG. 9 is an illustration depicting a technique to locate optimaldemodulation times for OFDM symbols according to an embodiment of theinvention.

DETAILED DESCRIPTION

[0017] Referring to FIG. 1, an embodiment 10 of an OFDM receiver inaccordance with the invention continuously performs a Discrete FourierTransform (DFT) to continuously demodulate a received OFDM signal. Inthis manner, as described below, the receiver includes a DFT engine 18that performs a sliding window DFT to continuously demodulate thereceived OFDM signal. More specifically, in some embodiments of theinvention, the DFT engine 18 continually performs DFTs on the receivedOFDM signal by effectively sliding a window of a fixed length in timeover the received OFDM signal. In this manner, this window slides intime over discrete time samples of the received OFDM signal, so that theDFT engine 18 calculates a DFT for each position of the window. Asdescribed below, in the course of calculating these DFTs, the DFT engine18 determines the optimal time interval for capturing a particular OFDMsymbol and selects one of the DFTs associated with this optimal timeinterval to extract, or derive, the OFDM symbol.

[0018] Referring to both FIGS. 1 and 2, regarding the specific structureof the receiver 10, the receiver 10 includes an antenna 12 that receivesan OFDM signal 51 (see FIG. 2) that includes OFDM symbols 52 (OFDMsymbols 52 a and 52 b, depicted as examples). Each symbol 52 isassociated with a different time slice, or slot, of the OFDM signal 51.The OFDM signal 51 is processed by analog receiving circuitry 14, andthe results are furnished to an analog-to-digital converter (ADC) 16that furnishes a digital indication (i.e., discrete time samples) of theOFDM signal 51. This analog indication is processed by the DFT engine 18in a manner that continuously computes a sliding window DFT.

[0019] More particularly, in some embodiments of the invention, the DFTengine 18, for each new discrete time sample, generates a DFT based ondiscrete time samples that are contained in a particular window 60.Thus, each successive DFT is computed using a window 60 that includesone new sample and one less sample that were used in the computation ofthe previous sliding window DFT. As depicted in FIG. 2, the slidingwindow 60 eventually becomes substantially aligned with the particularOFDM symbol 52 to be demodulated. For example, the OFDM symbol 52 aaligns with the sliding window 60 a. Thus, the sliding window 60 a is inthe optimal position for demodulation of the OFDM symbol 52 a. The DFTthat is calculated using the time samples in the window 60 produces anindication of the demodulated OFDM symbol 52 a. Similarly, the slidingwindow 60 b is substantially aligned with the OFDM symbol 52 b. Asdescribed below, the DFT engine 18 determines which sliding window 60 toselect as the optimal time interval for the particular OFDM symbol 52(i.e., to select the window 60 that is synchronized to the OFDM symbol52), and the selected window 60 has a corresponding DFT that provides anindication of the demodulated OFDM symbol.

[0020] As depicted in FIG. 2, each sliding window DFT producescoefficients 64 corresponding to the output subcarriers of the OFDMsymbol and coefficients 66 that, as described below, correspond to pilottones that are used to find the optimal point for the demodulation of aparticular OFDM symbol 52. Thus, use of the sliding window DFT allowsthe OFDM subcarriers to be used in the synchronization process, asdescribed below.

[0021] Therefore, the demodulation technique that is performed by theDFT engine 18 provides continuous computation of the DFT of the receivedOFDM signal. This technique allows time synchronization and frequencysynchronization to be performed strictly in the frequency domain, whichoffers many advantages, including the benefits of the processing gainsfrom computation of the transform. In addition, the technique that isperformed by the DFT engine 18 also allows a particular demodulator toskip computation of subcarriers not intended for a particular user orterminal. This provides a reduction in the processing requirements forthe DFT engine 18, as described below.

[0022] The DFT engine 18, in some embodiments of the invention, includesa processor 25 that executes instructions, such as a program 22 that isstored in a memory 24 of the DFT engine 18. The program 22 causes theprocessor 25 to perform a technique 80 that is depicted in FIG. 3. Inthis manner, referring to FIG. 3, in the performance of the technique80, the DFT engine 18 calculates (block 82) the next sliding window DFT.After calculating the next sliding window DFT, the DFT engine 18determines (diamond 84) whether the associated window 60 is in anoptimal timing location to demodulate a particular OFDM symbol. If not,the DFT engine 18 calculates (block 82) the next sliding window DFT.Otherwise, the DFT engine 18 uses (block 86) the DFT to derive ademodulated OFDM symbol. This use may include the DFT engine 18 tagginga particular DFT result for later derivation of a particular OFDMsymbol. Subsequently, the DFT engine 18 returns to block 82 to calculatethe next sliding window DFT.

[0023] The extent of the mathematical operations that are performed inconventional OFDM receivers because of the processing of coefficientsthat are associated with non-used OFDM subcarriers becomes apparent whena signal flow diagram of the conventional FFT is examined. For example,FIG. 4 depicts a signal flow diagram for the computation of a Radix-twoFFT, a FFT used by conventional OFDM receivers. As shown, for an eightpoint Radix-two FFT, three stages 102, 104 and 106 are used to computethe FFT. Additional stages may be added to compute a larger FFT. Asdepicted in FIG. 4, each frequency coefficient (X₀, X₁, X₂ . . . X₇)that is provided by the last stage 106 depends on every discrete timevalue (x₁, x₂, x₃ . . . x_(n)) of the input vector. Thus, processing acoefficient for a particular subcarrier that is not used produces asignificant number of unnecessary mathematical operations.

[0024] In contrast to the conventional OFDM receiver, the receiver 10(FIG. 2) includes the DFT engine 18 that calculates the frequencycoefficients for each transformation pursuant to the signal flow diagram130 that is depicted in FIG. 5. The results of the signal flow diagram130 may be simplified down to the following mathematical relationship:

X _(f,k+1) =e ^(j2πf/N)·(X _(f,k) +x _(k+N) −x _(k)),  Equation (1)

[0025] where “X” indicates a particular subcarrier frequency coefficientat a particular time, as indexed by a particular subcarrier frequencycalled “f” and a coefficient “k” that indexes a particular slidingwindow 60 (FIG. 2). The coefficient “N” is the length, of the number ofdiscrete time samples in the window 60. The notation “x” denotes adiscrete time sample indexed by the “k” coefficient or “k+N”coefficient. As shown, each output frequency coefficient “X” is computedindependent of the other frequency coefficients. This permits unneededoutput computations to be skipped for unused subcarriers, thereby savingprocessing cycles for the DFT engine 18 and more efficient computationof the DFT.

[0026] As an example, a table 160 in FIG. 6 depicts a comparison of thetechnique 80 used by the DFT engine 18 with Radix-two FFT computations.In particular, the entries in column 162 are different numbers ofavailable OFDM subcarriers (assigned and unassigned); the entries incolumn 164 are the numbers of computations required by the Radix-two FFTcomputations for the different OFDM subcarriers; and the entries ofcolumn 166 define points where the calculations by the DFT engine 18 aremore efficient than the calculations of the Radix-two FFT. In thismanner, for the case where the number of assigned subcarriers (column162) does not exceed the values indicated in column 166, the techniqueprovided by the DFT engine 18 provides a computational benefit over theconventional FFT-based demodulation.

[0027] For example, if the total number of available subcarriers is 64(row 3 of column 162), then as long as six or less subcarriers areassigned, the DFT engine 18 is computationally more efficient than anengine that uses Radix-two FFT computations.

[0028] Thus, the technique that is used by the DFT engine 18 has thefollowing additional advantages over traditional techniques that use theFFT. First, the technique that is provided by the DFT engine 18 providesa flexibility in block size, i.e., the number of subcarriers that arecomputed. In this manner, because the subcarriers are each computedindependently in the sliding window DFT technique, a change in thenumber of subcarriers, either in total or for a particular terminal, iseasily accommodated. The number of subcarriers actually computed thuscan be any number without restrictions as to length of powers of two,primes or other algorithm-related limitations. Secondly, the slidingwindow DFT technique described herein permits faster acquisition. Inthis manner, because time and frequency synchronization may be donedirectly in the frequency domain at a greatly increased sample rate,acquisition time may be reduced significantly. This may be particularlyimportant since long acquisition time is a consequence of many of theconventional synchronization algorithms. Thirdly, changes in the samplerate relative to the OFDM sample, regardless of the number ofsubcarriers or the number of subcarriers being processed, may beaccommodated by adjusting the phase of the coefficient in each outputcalculation. No address bit reverse processing or buffering may berequired. Lastly, latency is reduced due to the technique provided bythe DFT engine 18. In this manner, the recursive nature of the techniquethat is used by the DFT engine 18 greatly reduces the latency. Therequired number of computations from the receipt of the last time domainsample in the OFDM symbol to obtain the demodulated subcarriers is onthe order of “N” instead of on the order of “N*log₂(N).”

[0029] The sliding window technique that is used by the DFT engine 18may be derived, as described below. In this manner, for a vector x ofdimension N, the Discrete Fourier Transform of x is defined as:$\begin{matrix}{{X_{f} = {\sum\limits_{n = 0}^{N - 1}{x_{n} \cdot ^{{- {j2\pi}}\quad f\quad {n/N}}}}},} & {{Equation}\quad (2)}\end{matrix}$

[0030] where “n” is the time index and “f” is the frequency index.Adding an additional time index, k, which controls the slide of the DFTover multiple input windows of length N, yields a two-dimensionaldefinition of a sliding DFT as: $\begin{matrix}{{X_{f,k} = {\sum\limits_{n = 0}^{N - 1}{x_{n + k} \cdot ^{{- {j2\pi}}\quad f\quad {n/N}}}}},} & {{Equation}\quad (3)}\end{matrix}$

[0031] The DFT of the (k+1)th element can be rewritten as:$\begin{matrix}{{X_{f,{k + 1}} = {\sum\limits_{n = 0}^{N - 1}{x_{n + k + 1} \cdot ^{{- {j2\pi}}\quad f\quad {n/N}}}}},} & {{Equation}\quad (4)}\end{matrix}$

[0032] Substituting p=n+1, where the range of p is 1 to N yields:$\begin{matrix}{{X_{f,{k + 1}} = {\sum\limits_{p = 1}^{N - 1}{x_{p + k} \cdot ^{{- {j2\pi}}\quad f\quad {{n{({p - 1})}}/N}}}}},} & {{Equation}\quad (5)}\end{matrix}$

[0033] The summation may be changed by formally expressing the Nthcomponent separately and adding the p=0 case. The added case is thensubtracted formally as described in Equation 6 below. Consequently, therange of p is now 0 to N−1. $\begin{matrix}{{X_{f,{k + 1}} = {\left\lbrack {\sum\limits_{p = 0}^{N - 1}{x_{p + k} \cdot ^{{- {j2\pi}}\quad f\quad {{({p - 1})}/N}}}} \right\rbrack + {x_{k + N} \cdot ^{{- {j2\pi}}\quad f\quad {{({N - 1})}/N}}} - {x_{k} \cdot ^{{j2\pi}\quad {f/N}}}}},} & {{Equation}\quad (6)}\end{matrix}$

[0034] The single rotation exponential can be factored out as follows:$\begin{matrix}{{X_{f,{k + 1}} = {^{{j2\pi}\quad {f/N}} \cdot \left( {\left\lbrack {\sum\limits_{p = 0}^{N - 1}{x_{p + k} \cdot ^{{- {j2\pi}}\quad f\quad {{(p)}/N}}}} \right\rbrack + {x_{k + N} \cdot ^{{- {j2\pi}}\quad f\quad {N/N}}} - x_{k}} \right)}},} & {{Equation}\quad (7)}\end{matrix}$

[0035] The exponential with the k+N term always has phase=2π and istherefore equal to 1, so: $\begin{matrix}{{X_{f,{k + 1}} = {^{{j2\pi}\quad {f/N}} \cdot \left( {\left\lbrack {\sum\limits_{p = 0}^{N - 1}{x_{p + k} \cdot ^{{- {j2\pi}}\quad f\quad {p/N}}}} \right\rbrack + x_{k + N} - x_{k}} \right)}},} & {{Equation}\quad (8)}\end{matrix}$

[0036] Note that the summation is the DFT of the kth vector, and theexpression can be rewritten as Equation (1), above. This yields arecursive structure where the (k+1)th DFT is computed using the outputof the kth DFT. The difference of the oldest and newest time inputs iscomputed and added to the output of each element of the previous DFT.Each DFT output is then individually multiplied by a rotational constantthat is fixed for each frequency bin. The computation of thesliding-window DFT can be initialized by starting with the input andoutput buffers set to all zeros. As k increments the new data istrickled in until the input buffer is full, at which point the outputbecomes valid.

[0037] Referring to FIG. 7, in some embodiments of the invention, thereceiver 10 may communicate (over a wireless link 202 or a cable-basedlink, as examples) via an OFDM transmitter 200. The transmitter 200includes a processor 214 that executes instructions, or a program 212,that is stored in a memory 210 of the transmitter 200. In response tothe processor 214 executing the program 212, the program 212 causes theprocessor 214 to perform a technique 220 that is depicted in FIG. 8. Inthis manner, in this technique 220, the transmitter 200 insertsinformation into the OFDM signal that aids the receiver 10 insynchronizing demodulation of the OFDM symbols using the above-describedsliding window DFT technique.

[0038] More particularly, referring to FIG. 8, in the technique 220, theprocessor 214 scrambles (block 224) pilot tones for a particular OFDMsymbol 52 a (see FIG. 9) using a pilot code, such as a pilot codedenoted by the suffix “A,” in particular example. After scrambling thepilot tones, the processor 214 generates (block 226) the OFDM symbol 52a. Subsequently, the processor 200 scrambles (block 228) pilot tones forthe OFDM 52 b (see FIG. 9) using a different pilot code (demoted by thesuffix “B,”) in this example. The processor 200 then generates (block230) the OFDM symbol 52 b. Thus, pursuant to the technique 220, thetransmitter 200 uses different pilot tones for adjacent (in time) OFDMsymbols for purposes of aiding in the synchronization for thedemodulation of these symbols, as described below.

[0039] In this manner, adjacent OFDM symbols in time are assigneddifferent known scrambling codes, so that the coefficients of adjacentsliding DFT windows may be correlated to identify the individual symbolsand the best point in time to demodulate them. FIG. 9 further depicts anillustration 150 of a technique that may be applied to each slidingwindow DFT 60. As shown, each sliding window DFT produces coefficients64 that are related to the output subcarriers and coefficients 66 thatare related to the pilot tones that are associated with a particularOFDM symbol. The coefficients 64 and 66 of a particular sliding windowDFT 60 are correlated with the pilot code A (via a correlator 252) andthe pilot code B (via a correlator 258) to produce two respectivecorrelation signals 260 and 262. In response to the sliding window DFTdemodulating pilot tones that are scrambled via the pilot code A, thesignal 260 peaks (as indicated by 160 a) to indicate detection of thepilot code A. Similarly, in response to a particular sliding window DFTdemodulating pilot tones scrambled via the pilot code B, the signal 262peaks (as indicated by the peak 262 a) to indicate detection of thepilot code B.

[0040] Thus, in this manner, if the pilot codes A and B are used toscramble pilot tones in adjacent OFDM symbols, then the occurrence ofthe OFDM symbols 52 may be detected via the signals 260 and 262. Thisallows discrimination between adjacent symbols 52, as well as locationof the optimal sampling point for demodulation. As an example, the pilottones may be binary phase shift keyed (BPSK) modulated using a 15 bitpseudo noise (PN) sequence that is shifted four bits between adjacentsymbols with a single bit added. However, it is certainly not necessaryto use PN sequences for discrimination, and any disparate sequences witha reasonable Hamming distance will provide good performance. Thecorrelator output signal peaks (such as the peaks 260 a and 262 a) thatcorrespond to the optimal timing locations are identified by the lowoutput variance on either side of the peak.

[0041] Thus the advantages of the above-described synchronizationtechnique includes one or more of the following. First, theabove-described synchronization permits faster acquisition. In thismanner, because time synchronization may be done directly in thefrequency domain at a greater increased sampling rate, acquisition timemay be reduced significantly. This technique offers the potential offirst symbol acquisition or burst acquisition of OFDM symbols, aparticularly important advantage since long acquisition time is aconsequence of many of the commonly used synchronization algorithms.Secondly, because the different pilot codes may be easily discriminated,it is possible to use the synchronization technique for multiple access.In this manner, a particular terminal may correlate pilots against aunique code assigned only to it, such that it does not demodulate OFDMsymbols that are destined for other terminals. A third advantage is thatthe location of the optimal timing location reduces timing-error-induced“twist” in the demodulated signal. This eases the burden of the channelestimation and equalization algorithms so that more performance marginis available for correcting channel impairments rather than twist due tosynchronization errors. Fourthly, latency is reduced. In this manner,when the optimal timing location is detected, the data is immediatelyavailable for channel estimation and equalization.

[0042] While the invention has been disclosed with respect to a limitednumber of embodiments, those skilled in the art, having the benefit ofthis disclosure, will appreciate numerous modifications and variationstherefrom. It is intended that the appended claims cover all suchmodifications and variations as fall within the true spirit and scope ofthe invention.

What is claimed is:
 1. A method comprising: receiving a signalindicating a modulated symbol during a given time slice of the signal;performing sliding window frequency transformations of the signal, eachsliding window transformation being associated with a different timeinterval of the signal; selecting one of the time intervals tocorrespond to said time slice; and using the result of the frequencytransformation associated with the selected time interval to obtain anindication of the demodulated symbol.
 2. The method of claim 1, whereinthe selecting comprises: correlating the sliding window transformationswith a first pilot code; correlating the sliding window transformationswith a second pilot code; and comparing the results of the correlationswith the first and second pilot codes to select said one of the timeintervals.
 3. The method of claim 2, wherein the first pilot code isassociated with the symbol, and the second pilot code is associated withanother symbol adjacent to the first symbol in time.
 4. The method ofclaim 2, wherein the comparing the results of the correlationscomprises: finding a time interval between where the correlations peak.5. The method of claim 1, wherein the performing the sliding windowtransformations comprises: for each transformation, adding at least oneadditional sample of the signal to the transformation as compared to aprevious transformation and removing at least one sample used in theprevious transformation.
 6. The method of claim 1, wherein performingthe sliding window frequency transformations comprises: sampling thesignal to produce samples at different points in time; creating a windowto select a predetermined number of the samples within the time intervalassociated with the sliding window transformation; and performing one ofthe sliding window transformations for each window.
 7. The method ofclaim 6, wherein performing each sliding window transformationcomprises: advancing the window in time before performing the nextsliding window transformation.
 8. The method of claim 7, wherein theadvancing comprises: advancing the window in time by a predeterminednumber of sampling periods.
 9. The method of claim 1, wherein the signalcomprises an Orthogonal Frequency Division Multiplexing signal.
 10. Amethod comprising: generating a modulated signal, the signal comprisinga first modulated symbol and a second modulated symbol adjacent to thefirst modulated symbol in time; scrambling first pilot tones associatedwith the first modulated symbol with a first pilot tone; and scramblingsecond pilot tones associated with the second modulated symbol with asecond pilot tone to indicate a time interval in which to demodulate thefirst modulated symbol from the signal.
 11. The method of claim 10,wherein the modulated signal comprises an Orthogonal Frequency DivisionMultiplexing signal.
 12. The method of claim 10, further comprising:transmitting the modulated signal.
 13. A method comprising: receiving asignal containing a modulated symbol; performing frequencytransformations of the signal; correlating the frequency transformationswith a first pilot code; correlating the frequency transformations witha second pilot code; and comparing the results of the correlations withthe first and second pilot codes to select one of the frequencytransformations to obtain an indication of the demodulated symbol. 14.The method of claim 13, wherein the first pilot code is associated withthe symbol, and the second pilot code is associated with another symboladjacent to the first symbol in time.
 15. The method of claim 13,wherein the comparing of the results of the correlations comprises:finding a time interval between where the correlations peak.
 16. Themethod of claim 13, wherein the signal comprises an Orthogonal FrequencyDivision Multiplexing signal.
 17. A receiver comprising: circuitry toreceive a signal indicating a modulated signal associated with a giventime slice of the signal; and an engine to: perform sliding windowfrequency transformations of the signal, each sliding windowtransformation being associated with a different time interval of thesignal; select one of the time intervals to correspond to said givenperiod of time; and use the result of the frequency transformationassociated with the selected time interval to obtain an indication ofthe demodulated symbol.
 18. The system of claim 17, wherein the enginecorrelates the sliding window transformations with a first pilot code,correlates the sliding window transformations with a second pilot code,and compares the results of the correlations with the first and secondpilot codes to select said one of the time intervals.
 19. The system ofclaim 18, wherein the first pilot code is associated with the symbol,and the second pilot code is associated with another symbol adjacent tothe first symbol in time.
 20. The system of claim 18, wherein the enginecompares the results of the correlations by finding a time intervalbetween where the correlations peak.
 21. The system of claim 17 whereinthe engine performs the sliding window transformations by for eachtransformation, adding at least one additional sample of the signal tothe transformation as compared to a previous transformation and removingat least one sample used in the previous transformation.
 22. The systemof claim 17, wherein the engine samples the signal to produce samples atdifferent points in time and creates a window to select a predeterminednumber of the samples within the time interval associated with thesliding window transformation.
 23. The system of claim 22, wherein theengine advances the window in time before performing the next slidingwindow transformation.
 24. The system of claim 23, wherein the engineadvances the window in time by one sampling period.
 25. The system ofclaim 17, wherein the signal comprises an Orthogonal Frequency DivisionMultiplexing signal.
 26. A apparatus comprising: circuitry to receive asignal containing a modulated symbol; and an engine to: performfrequency transformations of the signal, correlate the frequencytransformations with a first pilot code, correlate the frequencytransformations with a second pilot code, and compare the results of thecorrelations with the first and second pilot codes to select one of thefrequency transformations to obtain an indication of the demodulatedsymbol.
 27. The apparatus of claim 26, wherein the first pilot code isassociated with the symbol, and the second pilot code is associated withanother symbol adjacent to the first symbol in time.
 28. The apparatusof claim 26, wherein the engine finds a time interval between where thecorrelations peak to select one of the frequency transformations. 29.The apparatus of claim 26, wherein the signal comprises an OrthogonalFrequency Division Multiplexing signal.